Migrant Business Ownership: Power Analysis of Statistical Significance

A 2012 study based on Current Population Survey (CPS) data from the U.S. Census Bureau found that the existing business-ownership rate is higher for migrants than native-born adults in America: 10.5% of the migrant workforce own a business, compared with 9.3% of the native-born labor force.

a. Fill in the following table for the power for the given alternatives. Assume that 9.3% of the native-born labor force own a business.

migrant significance number of proportion level power observations 0.105 0.05 0.95 3177 0.105 0.01 0.95 4837 0.105 0.05 1000 0.181 0.105 0.05 2000 0.746 0.120 0.05 0.95 2299 0.120 0.01 0.95 3518 0.120 0.05 1000 0.960 0.120 0.05 2000 1.000

See D2L for an example of how to do a power calculation in R (first entry of table):

Write on your whiteboard 'more' or 'less' based on the statements in b and c.

b. If we are willing to have a smaller significance level, we can get the same power with 'more' observations. c. If a higher proportion of migrants own businesses, then 'less' observations are needed to maintain the same power.